Where is the Hazard Relay located?

You need the factory style switch if you want the hazards to operate. That is because it does more than just turn on power. It connects both sides of the lighting system to the single hazard flasher, so you get 4 corner flashing lights. However, if you are just trying to get power to the hazard system you run power to a flasher can and from the can out to the Brown wire that feeds the multi-function switch.